The present invention relates generally to particle characterization; and more particularly to an apparatus and non-intrusive methods for characterizing particles based on scattering matrix elements measurements made using elliptically polarized radiation, and methods of compiling a database of theoretical data for use therein.
In many modern materials and manufacturing processes such as printers, copiers, fluidized bed reactors, powder coating machines, ceramic coatings, etc, small particles play a significant role. The control, streamlining and overall efficiency of many of these modern processes may be significantly improved if the particles involved in the processes are able to be precisely characterized. Determining whether particles resulting from a manufacturing process are spheroids as intended, for example, or whether the resulting particles actually agglomerated during the process may be critical to the overall success/efficiency of the process. These modern processes may be further enhanced by the ability to characterize particles such that the presence of undesirable particles and their respective adverse effects may be minimized. Examples of these processes include the fabrication of solid-state devices wherein the presence of sub-micron size contaminants in a fabrication area can have an enormous detrimental impact on the devices, metallurgical manufacturing wherein airborne dust particles create a significant fire and explosion hazard, and combustion chambers wherein a failure to burn soot particles including agglomerates allows their escape into the environment.
Recent advances in diverse disciplines, such as biological, pharmaceutical, environmental, and combustion systems as well as atmospheric and oceanographic remote sensing have created a much wider range of applications of and need for better characterization of particles in general. One of the most often used methods to characterize these particles includes optical diagnostics in which the particles are subjected to incident electromagnetic waves from a radiation source, and their responses or the scattered radiation are recorded. By comparing the recorded response against responses of previously physically measured particles, some characteristics of the particles may be estimated. These estimates, however, are only as accurate as the physically measured data which itself is difficult to accurately obtain at these small particle sizes. Although generally effective in confirming the presence of known or expected particle types, these methods of characterization are significantly limited and certainly may not be used to characterize unknown particle types and/or unexpected particles resulting from agglomeration during a process or the like.
Thus, as demonstrated by the limitations and disadvantages of the prior art methods of characterizing particles, there is a need identified for an improved more robust method of characterizing particles and mixtures of particles of any size, shape, and size and/or shape distribution without a reliance on measured data which is often unavailable, inaccurate, or incomplete for the particles being characterized.
The present invention meets these needs by providing a non-intrusive method of characterizing particles or particle systems through inverse analysis of experimental data based on measurements using elliptically polarized radiation. A database of theoretical absorption and scattering data sets for particles is compiled. Optimum settings for an experimental test to gather an experimental absorption and scattering data set are determined and the experimental test is conducted. The experimental absorption and scattering data set is then compared to the theoretical absorption and scattering data sets of the database of theoretical absorption and scattering data sets in order to determine an absorption and scattering data set which differs the least from the experimental absorption and scattering data set in order to characterize the particles.
The particles referred to throughout the present application are herein defined to include fine particles and/or agglomerates of any size, size distribution, and shape. More specifically, the fine particles may include homogeneous spheres, radially inhomogeneous spheres, homogeneous cylinders, radially inhomogeneous cylinders, oblate spheroids, prolate spheroids, and/or ellipsoids, hollow particles, nanostructures, and nanocrystals, and the agglomerates may include irregular shaped structures, fractal-like agglomerates, fluffy or compact agglomerates, and hollow particles.
In accordance with a first aspect of the present invention, the step of compiling the database of theoretical absorption and scattering data sets for the particles may include the steps of calculating an interaction of a theoretical incident planar wave having a wavelength (xcex) on each monomer of the particle having a diameter (d) and a complex index of refraction (m=nxe2x88x92ik), and interactions of portions of the theoretical incident planar wave scattered by each remaining monomer of the particle using Maxwell""s equations as is known in the art. The diameter (d) of each monomer may be an effective diameter based on a volume of the monomer. For irregular shaped particles, the particle may be divided into volumes which are themselves converted into effective spherical diameters. For the remaining particles types, the monomer diameter may be made equivalent to the size of the small spheres which make up the agglomerate or the like. The calculated interactions may then be summed for each monomer of the particle and a distribution of the theoretical incident planar wave scattered by the particle and an absorption of the theoretical incident planar wave by the particle determined. The method may further comprise the step of determining scattering matrix elements for the particle based on the determined distribution of the theoretical incident planar wave scattered by the particle and the determined absorption of the theoretical incident planar wave by the particle.
In accordance with another aspect of the present invention, the step of compiling the database of theoretical absorption and scattering data sets for the particles preferably includes the additional step of repeating the aforementioned steps of calculating an interaction of a theoretical incident planar wave and interactions of portions of the theoretical incident planar wave, summing the calculated interactions, determining a distribution of the theoretical incident planar wave scattered by the particles and an absorption of the theoretical incident planar wave by the particles, and determining scattering matrix elements for every possible combination of wavelength (xcex), and particle characteristic including diameter (d), complex index of refraction (n), and absorption index (k). For particles which include fractal agglomerates, the aforementioned steps are further repeated for every possible combination of fractal dimension Df and prefactor Kf.
In accordance with still another aspect of the present invention, the step of determining optimum settings for the experimental test to gather the experimental absorption and scattering data set further includes the step of estimating characteristics of the particles being characterized. The estimated characteristics of the particles being characterized may include data obtained from a transmission electron microscope, a scanning electron microscope, or an atomic force microscope, for example. A wavelength of a theoretical elliptically polarized radiation is selected based on the estimated characteristics of the particles being characterized and a theoretical set of polarizers and retarders are selected based on the selected wavelength. The step of determining optimum settings may further include the step of selecting an orientation for optical axes of the polarizers and retarders in the theoretical set.
Utilizing the selected theoretical set of polarizers and retarders, an intensity of the theoretical elliptically polarized radiation scattered by the particles being characterized at a detection plane at different scattering angles may be determined. These steps may be repeated for each selected orientation of the polarizers and retarders in the theoretical set. Based on the intensity of the theoretical elliptically polarized radiation scattered by the particles, orientations for the optical axes of the polarizers and retarders in the theoretical set which provide sufficiently high signal-to-noise ratios may be selected as the optimum settings for use in the experimental test.
According to another aspect of the present invention, the step of determining optimum settings may further include the step of conducting a preliminary experimental test. The preliminary experimental test may be conducted when insufficient data is available regarding the characteristics of the particles being characterized, for example, when no information or data is available for the particles to be characterized or if the particles are composed of combinations of different particle types and information or data for the combination or at least some of the particle types which form the combination is unavailable.
As described above, the steps of selecting a wavelength of an elliptically polarized radiation based on a set of estimated characteristics of the particles being characterized, selecting a set of polarizers and retarders each having an optical axis based on the selected wavelength, and selecting an orientation for the optical axes of said polarizers and retarders in said set are similarly established prior to conducting the preliminary experimental test. Conducting the preliminary experimental test includes the steps of directing elliptically polarized radiation having the selected wavelength toward the particles to be characterized, modulating the polarization of the radiation before and after the radiation is incident on the particles, and detecting radiation scattered by the particles to be characterized at at least one scattering angle. The steps of directing, modulating, and detecting scattered radiation may be repeated any number of times sufficient to collect the necessary data. The orientation of the optical axes of the polarizers and retarders in the set are preferably adjusted prior to each repetition of the noted directing, modulating, and detecting steps.
The polarization of the radiation before and after the radiation is incident on the particles may be modulated utilizing appropriately positioned polarizers and retarders in the sets. Preferably, lenses, apertures, and additional polarizers and retarders may be utilized to direct or modulate the radiation either before or after the radiation is incident on the particles. An intensity of the modulated radiation may be detected using one or more detectors positioned at different scattering angles. The detector preferably generates an output dependent upon the intensity of the scattered radiation at the present scattering angle.
In accordance with yet another aspect of the present invention, equations representing the outputs of the detectors resulting from the preliminary experimental test may be solved simultaneously in order to determine the preliminary experimental absorption and scattering data set. The preliminary experimental absorption and scattering data set is then compared to the theoretical absorption and scattering data sets of the database in order to determine an absorption and scattering data set which differs the least from the preliminary experimental absorption and scattering data set.
According to yet another aspect of the present invention, the estimated characteristics of the particles being characterized may be replaced with new characteristics corresponding to the preliminary experimental absorption and scattering data set. Additionally, the preliminary experimental test and replacement of the estimated characteristics or the previous replacement characteristics may be repeated any number of times in order to improve the accuracy of the estimated characteristics for use in the step of determining the optimum settings.
In accordance with another aspect of the present invention, the step of conducting the experimental test may include the steps of directing elliptically polarized radiation having a selected wavelength toward the particles to be characterized, modulating the polarization of the radiation before and after the radiation is incident on the particles to be characterized, and detecting radiation scattered by the particles to be characterized at at least one scattering angle. The steps of directing, modulating, and detecting the elliptically polarized radiation are repeated six times in accordance with the present preferred method, however, the steps may be repeated fewer or more times depending on the type of particles or combinations of particles being characterized and/or the amount of information known about the particles.
As in the preliminary experimental test, the polarization of the radiation before and after the radiation is incident on the particles may be modulated utilizing appropriately positioned polarizers and retarders. Each of the polarizers and retarders have optical axes which are preferably established at a first predetermined orientation or optimum setting before conducting the experimental test. The optical axes of at least one of the polarizers and retarders may be adjusted to a second predetermined orientation between successive repetitions of the directing, modulating and detecting steps. The modulated radiation may be detected using one or more detectors positioned at different scattering angles. The detectors preferably generate an output based on the intensity of the detected radiation. Equations representing the outputs of the detectors resulting from the experimental test may be solved in order to determine an experimental absorption and scattering data set. The experimental absorption and scattering data set is then compared to the theoretical absorption and scattering data sets of the database in order to determine an absorption and scattering data set which differs the least from the preliminary experimental absorption and scattering data set.
In accordance with another aspect of the present invention, the step of conducting an experimental test may be repeated at least once utilizing elliptically polarized radiation having a different wavelength in order minimize errors. More specifically, repeating the experimental test utilizing radiation having a different wavelength avoids errors which may be contributed to particles having significant absorption properties at specific wavelengths. The first experimental data set may be compared to at least one subsequent data set in order to insure the integrity of the experimental data set to be compared to the theoretical absorption and scattering data sets of the database. If a discrepancy between the experimental data sets is determined, additional experimental tests may be conducted utilizing radiation having another different wavelength in order to determine which set of experimental data is not affected by the significant absorption of the incident radiation by the particles.
Additional error minimization techniques may also be utilized including correcting the outputs of the detectors to remove interface and multiple scattering effects which may cause modulation of the elliptically polarized radiation. This may be accomplished, for example, by multiplying the outputs of the detectors by a corrective function selected to remove the noted interface and multiple scattering effects as is known in the art.
Another non-intrusive method of characterizing particles through inverse analysis of experimental data based on measurements made using elliptically polarized radiation includes the steps of conducting an experimental test utilizing predetermined optimized settings to obtain an experimental absorption and scattering data set, and comparing the experimental absorption and scattering data set to theoretical absorption and scattering data sets of a database in order to determine an absorption and scattering data set which differs the least from the experimental absorption and scattering data set. Preferably, the database of theoretical absorption and scattering data sets for the particles being characterized and the optimum settings for the experimental test have been theoretically or experimentally predetermined.
According to a second aspect of the present invention, an apparatus for characterizing particles through a non-intrusive inverse analysis of experimental data based on measurements using elliptically polarized radiation comprises a radiation source for generating elliptically polarized radiation having a wavelength (xcex), a plurality of polarizers and retarders each having an optical axis for modulating the elliptically polarized radiation before and after the radiation is incident on the particles, and at least one detector for detecting radiation scattered by the particles and generating an output. The apparatus further includes a controller for adjusting an orientation of the optical axis of at least one of the polarizers and retarders, and a processor for receiving the output from the detector, generating an experimental absorption and scattering data set based on the output of said at least one detector, and comparing the experimental absorption and scattering data set to theoretical absorption and scattering data sets in order to determine an absorption and scattering data set which differs the least from the experimental absorption and scattering data set in accordance with the above-described methods.
In accordance with another aspect of the present invention, the apparatus may include a rotary stage for supporting the particles, the polarizers and retarders, and/or the detector. Additionally, fiber optic cables and holders may be provided for directing the elliptically polarized radiation from the radiation source toward the particles and/or for collecting radiation scattered by the particles and modulated by the polarizers and retarders for directing to the detector. A motor such as stepper motor or other suitable motor may be provided for driving the rotary stage in response to control signals provided by the controller. In addition, the processor of the apparatus may be further programmed to generate the theoretical absorption and scattering data sets and/or determine an orientation for the polarizers and retarders in accordance with the methods described above.
In accordance with still another aspect of the present invention, a plurality of selectable polarizer and retarder sets may be mounted on a moveable platform controlled by the controller. In this alternate embodiment of the present preferred apparatus, an orientation of the optical axes of the polarizers and retarders in the polarizer and retarder sets mounted on the moveable platform are fixed. Rather than utilizing a controller to adjust the orientation of adjustable polarizers and retarders, the polarizers and retarders are selected by moving the platform based on their fixed orientations. In accordance with the broadest teachings of the present invention, any number of polarizer and retarder sets may be mounted on the moveable platform for selection by the processor.
Additional advantages, and other novel features of the invention will be set forth in part in the description that follows and in part will become apparent to those skilled in the art upon examination of the following or may be learned with the practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.